An electron spin resonance study has been made on lysozyme in. frozen aqueous solutions irradiated with $_{60}Co$ r-rays in air at $77^{circ}K.$ Water resonances are dominant when the concentration and the temperature are both below 20% and $130^{circ}K$ respectively. More solute radicals are produced in the solution of higher concentration. Majority of the solute radicals results from direct hit of the radiation. The same types of radicals are induced at $77^{circ}K$ whether the substances are irradiated in the dry state or in frozen aqueous solution. Based on these results, it is assumed that the number of ESR centers produced by the secondary intermolecular radical reacions and stabilized in aqueous solutions may depend on the concentration of the solution, and the presence of water may facilitate the secondary radical reactions occuring in the solute molecules after heat treatment. Majority of the solute radicals above around $193^{circ}K$ are believed to react with oxygen to form peroxytype radicals. However, when the solution is subiected to heat-treatment at $265^{circ}K$ after irradiation at $195^{circ}K$ the peroxy-type resonance was not observed, suggestin that an appreciable amount of oxygen is condensed into the ice, at $77^{circ}K.$ in addition to the oxygen that has already been dissolved in solution and react with solute free radicals during the process of heat-treatment. When the solution contains $H_2O_2$, no water resonance but $HO_2$, type resonance was observed probably indicating that the radiation-induced OH radicals are trapped in $H_2O_2$ aggregates and react readily with $H_2O_2$ molecules to poroduce $HO_2$ type radicals even at $77^{circ}K.$